Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model

• Autor(a) principal: PEREIRA,A.P.P.
• Data de Publicação: 2017
• Outros Autores: FERNANDES,J.P., ATMAN,A.P.F., ACEBAL,J.L.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000200305
• topic: anomalous diffusion; fractional diffusion equation; calibration

ABSTRACT We address the problem of subdiffusion or normal diffusion to perform a calibration between simulations parameters and those from a subdiffusive model. The theoretical model consists to a generalized diffusion equation with fractional derivatives in time. The data generated by simulations represents continuous-time random walks with controlled mean waiting time and jump length variance to provide a full range of cases between subdiffusion and normal diffusion. From simulations, we compare the accuracy of two methods to obtain the diffusion constant and the order of fractional derivatives: the analysis of the dispersion of the variance in time and an optimized fitting of the histograms of positions with theoretical model solutions. We highlight the connection between the parameters of the simulations those of theoretical models.